Alan

Do we assume that theta is in degrees?  If so this becomes

(θ*180/pi - 90)*pi = 180*sin(θ)

  or  (θ - pi/2) = sin(θ)  

where θ is in radians.

However, there is no elegant algebraic solution here.  Use a numerical method, such as Newton-Raphson or simple repeated substitution (say θ₀ = 1, θ_n = sin(θ_n-1) + pi/2).

Here's the trig substitution approach:

$${\mathtt{f}} = {\frac{{\mathtt{2.998}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{8}}}}{\left({\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{-{\mathtt{6}}}\right)}} \Rightarrow {\mathtt{f}} = {\mathtt{74\,950\,000\,000\,000}}$$

or f = 0.7495*10¹⁴ Hz

The wavelength should have 10^-6 NinjaDevo, not 10⁺⁶.

One solution is: L=1  A=9  S=2  E=6  R=5  H=4

LASER + REAL

$${\mathtt{19\,265}}{\mathtt{\,\small\textbf+\,}}{\mathtt{5\,691}} = {\mathtt{24\,956}}$$ 

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24956

There are 7 more solutions!

Anonymous posted: (2x + 1)(x + 3) = 2(x + 1/2)(x + 3) = (2x + 6)(x + 1/2).

Correct! This shows the two polynomials are the same (though note that the original question was to find the values of a, b and c - so there are two sets of answers to the original question).

If the volume of the tank is, say, V litres, then

A fills it at a rate of V/3 litres/hour

B fills it at a rate of V/4 litres/hour

C fills it at a rate of V/6 litres/hour

So A+B+C would fill it at a rate of V/3 + V/4 + V/6 = 3V/4 litres/hour

Time taken = V/(3V/4) = 4/3 hours  or 1hour 20 minutes. 

Use the calculator on this site - it has a square root button.

You need to know the mass of the body with the fat.  Then express the percentage as a fraction and multiply by the mass of the body in question expressed in grams.

If you have an equation of a straight line in the form y = m*x + c where m and c are constants then the slope is given by m and the y-intercept is given by c. In this case m = 3, so that is the slope of your line.

Seems to me there are two sets of solutions here, unless I've screwed up somewhere (always a distinct possibility!). See below: